(adsbygoogle = window.adsbygoogle || []).push({}); Producing the Ricci tensor

On a pseudo-Riemannian manifold we can contract the Riemann curvature tensor to form the Ricci tensor. In this process of contraction we sum over two indices to make a (3-1)-tensor into a (2-0)-tensor. My question is, why must we contract two indices? Why cant we contract one index to form a (3-0)-tensor or a (2-1)-tensor, etc...

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# Producing a Ricci tensor

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